Let (M, g) be a compact Riemannian n-dimensional manifold with umbilic boundary It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean curvature hypersurface. In this paper we prove that these metrics are a compact set in the case of low dimensional manifolds, that is n = 6, 7, 8, provided that the Weyl tensor is always not vanishing on the boundary.

A compactness result for scalar-flat metrics on low dimensional manifolds with umbilic boundary

Ghimenti, Marco G.
;
Micheletti, Anna Maria
2021

Abstract

Let (M, g) be a compact Riemannian n-dimensional manifold with umbilic boundary It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean curvature hypersurface. In this paper we prove that these metrics are a compact set in the case of low dimensional manifolds, that is n = 6, 7, 8, provided that the Weyl tensor is always not vanishing on the boundary.
Ghimenti, Marco G.; Micheletti, Anna Maria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1112844
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